Cancel voltage offset of operational amplifier

ABSTRACT

A system according to examples of the present disclosure includes a battery charger electrically coupled to a battery and a battery charging circuit. The battery charging circuit includes an operational amplifier having a negative input to receive a pre-bias voltage, a positive input, an output, and a voltage offset. The battery charging circuit also includes a charge controller having an analog-to-digital converter to receive a voltage output from the output of the operational amplifier and a voltage supply to supply a voltage input into the positive input of the operation amplifier to cancel the voltage offset of the operational amplifier. In the example, the voltage output of the charge controller is a function of the voltage input of the charge controller.

BACKGROUND

Many computing systems such as laptops, tablets, mobile phones, andother similar systems utilize batteries to receive power. As thecomputing systems function, the batteries are drained. Consequently, thebatteries either need to be replaced or recharged from time to time sothat the computing systems can continue to function.

BRIEF DESCRIPTION OF THE DRAWINGS

The following detailed description references the drawings, in which:

FIG. 1 illustrates a block diagram of a circuit for regulating batterycharge current for a computing system by generating a signal bias tocancel the voltage offset of an operational amplifier using a chargecontroller according to examples of the present disclosure;

FIG. 2 illustrates a plot of the calibrated circuit offset biasaccording to examples of the present disclosure;

FIG. 3 illustrates a flow diagram of a method for regulating batterycharging current according to examples of the present disclosure; and

FIG. 4 illustrates a flow diagram of the calibration process of themethod for regulating current of FIG. 3 according to examples of thepresent disclosure.

DETAILED DESCRIPTION

Charging the battery of a computing system such as a laptop, tablet,mobile phone, or other similar system provides mobility and continuedusability of the systems. For example, many users of these computersystems utilize such computing systems while away from a steady powersource. However, the batteries drain over time as a result of use of thesystems. As such, the batteries need to be recharged from time to time.

To recharge the battery for a computing system, it may be desirable tosend a known current through the battery. In this way, the battery maybe charged at a preferred rate. That is, the battery may be charged asfast as possible without degrading the battery. If the battery ischarged too quickly, the integrity of the battery may be compromised,causing the battery to experience a failure, a shortened usablelifespan, or a catastrophic event. However, charging the battery tooslowly is inconvenience for the user of the computing system because theuser cannot use the system until the battery is recharged (at leastpartially).

Currently, computing systems may implement operational amplifiers toregulate the battery charging voltage or current. For example, computingsystems may implement an error correcting circuit having an operationalamplifier in which a reference signal is fed into the positive terminalof the operational amplifier and a feedback signal is fed into thenegative terminal of the operational amplifier. However, the voltageoffset inherent in operational amplifiers result in less than idealbattery charging current control. Previous solutions include utilizing amore expensive, low-offset operational amplifier or a more expensive,dedicated current sense amplifier to provide an optimal charge to abattery. In addition to being expensive, the voltage offset of theoperational amplifiers may vary with age and/or operating conditions.Other implementations for providing an optimal battery charge mayutilize an existing calibration method to characterize the amplifier byelectrically disconnecting it from the intended application, connectingand applying a test signal, recording results, and reconnecting it tothe intended application. However, this approach requires either theinclusion of extra switches and control signals on a computing system'sprinted circuit assembly (PCA), or a special in-circuit test processduring manufacture that is enabled by additional PCA components.

Various implementations are described below by referring to severalexamples of regulating battery charge current by generating a signalbias to cancel the voltage offset of a current regulator using anembedded controller. A system according to examples of the presentdisclosure includes a battery charger electrically coupled to a batteryand a battery charging circuit. The battery charging circuit includes anoperational amplifier having a negative input to receive a pre-biasvoltage, a positive input, an output, and a voltage offset. The batterycharging circuit also includes a charge controller having ananalog-to-digital converter to receive a voltage output from the outputof the operational amplifier and a voltage supply to supply a voltageinput into the positive input of the operational amplifier to cancel thevoltage offset of the operational amplifier. In the example, the voltageoutput of the charge controller is a function of the voltage input ofthe charge controller.

The techniques described herein enable very accurate regulation usinglow-cost operational amplifiers. Moreover, small charge currents can beaccurately controlled using the low-cost operational amplifiers. Theseand other advantages will be apparent from the description that follows.

FIG. 1 illustrates a block diagram of a circuit 110 for regulatingbattery charge current for a computing system 100 by generating a signalbias to cancel the voltage offset V_(OS) of an operational amplifier 120using a charge controller 130 according to examples of the presentdisclosure. FIG. 1 includes particular components, modules, etc.according to various examples. However, in different implementations,more, fewer, and/or other components, modules, arrangements ofcomponents/modules. etc. may be used according to the teachingsdescribed herein. In addition, various components, modules, etc.described herein may be implemented as one or more software modules,hardware modules, special-purpose hardware (e.g., application specifichardware, application specific integrated circuits (ASICs), embeddedcontrollers, hardwired circuitry, etc.), or some combination of these.

It should be understood that the computing system 100 may include anyappropriate type of computing device, including for example smartphones,tablets, desktops, laptops, workstations, servers, smart monitors, smarttelevisions, digital signage, scientific instruments, retail point ofsale devices, video walls, imaging devices, peripherals, or the like.

In the example shown in FIG. 1, the computing system 100 includes abattery charger 102 electrically coupled to a battery 104 and a batterycharging control circuit 110. The battery charger 102 may represent anyappropriate variety of battery charger typically associated withcharging batteries such as battery 104. The battery charger receives avoltage input V_(IN) such as by plugging the battery charger 102 into anelectrical outlet or other suitable power source. The battery charger102 then supplies a charge current to the battery 104, which in turnsupplies power to the computing system 100.

The battery charging control circuit 110 regulates the charge currentsupplied by the battery charger 102 to the battery 104 through a controlsignal. By regulating the charge current supplied to the battery 104,the battery may be optimally charged. That is, the battery 104 may becharged at the fastest rate possible that remains advantageous to theintegrity of the battery 104.

The battery charging control circuit 110 includes an operationalamplifier (or “op amp”) 120, a charge controller 130 and an assortmentof resistors, capacitors, and voltage sources as shown in FIG. 1. Duringcalibration, the battery charging control circuit 110 operates byapplying a pre-bias voltage V₄ through R₄ as an input signal into thenegative terminal of op amp 120 as the reference signal and by applyinga programmable reference V₀ as the feedback signal into the positiveinput of the op amp 120. When regulation is achieved, the final value ofvoltage V₀ may be stored within the charge controller 130 as a voltagebias value. The voltage bias value is then applied during charging tocancel the voltage offset V_(OS) of the op amp 120 and the effect of thepre-bias voltage V₄ through R₄, and thus the voltage bias of the batterycharging control circuit 110.

Current sensing utilizes a low-value current sense resistor R_(i) togenerate a voltage signal from the charge current without dissipatingmuch power. This signal is the amplified to produce a signal that islarge enough to be used. An example is shown in the battery chargingcontrol circuit 110 of FIG. 1. The charge current passes through senseresistor R_(i), which generates a sense voltage V_(i). The sense voltageV_(i) is fed back into the op amp 120 through R₃, where it is comparedto voltage V₁, which may be a smaller voltage derived from a largervoltage V₀.

When charging, the voltage V₁ is set by the output voltage V₀ of aprogrammable digital-to-analog converter (DAC) or by a programmablepulse width modulator (PWM) signal collectively referred to as voltagesupply (VS) 132, which is contained within the charge controller 130.Capacitor C₁ filters the PWM signal, in examples, into a direct currentaverage. The op amp 120 senses the feedback voltage V_(i) through R₃ atthe negative input of the op amp 120 (V−), and compares it to thereference voltage V₁ at the positive input (for example) of the op amp120 (V+). The voltage difference between the positive and negativeterminals of the op amp 120 (V+) and (V−) is amplified and output asvoltage V₃, which drives other elements (e.g., transistor Q₁ andresistor R₅) to control the charging current. Resistor R₃ and capacitorC₂ control the amount, and frequency response, of the amplificationperformed by op amp 120. If the feedback V_(i) is greater than thereference V₁, then V₃ is reduced, which reduces the charge current,which reduces V_(i), thus regulating V_(i) virtually equal to V₁.Consequently, the charge current is regulated to the desired value(i.e., to a value that promotes fast battery charging while reducing anynegative effects on the battery).

The op amp 120 also includes a voltage offset V_(OS) which acts as asmall direct current error inside the amplifier. Such an error is commonwithin operational amplifiers and can vary depending on themanufacturing processes and tolerances used to manufacture the op amp,the operating conditions of the op amp, the age of the op amp, andcombinations of these and other factors. If the feedback signal issmall, such as the small voltage across a current sense resistor R_(i),the V_(OS) causes the op amp to regulate to the wrong level.

To accomplish this and to permit calibration of the battery chargingcontrol circuit 110, a pre-bias voltage V₄ is passed through resistor R₄into the negative terminal (V−) of the op amp 120. In examples, V₄ maybe an existing 5V or 3.3V voltage rail or other suitable voltage source.The pre-bias voltage V₄ may be greater than half the range of thevoltage offset of the op amp 120. For example, if the range of thevoltage offset of the op amp 120 is +/−9 millivolts, the pre-biasvoltage V₄ as it is received at the negative terminal (V−) of the op amp120 through resistor R₄ is greater than 9 millivolts. This enables thenegative terminal (V−) of the op amp 120 to receive a positive voltagecurrent offset that is greater than the op amp offset V_(OS).

In an example, a voltage offset V_(OS) of an op amp such as op amp 120may be +/−9 mV. In this example, a voltage V₄ is passed through resistorR₄, which causes a current to be sent into resistor R₃, causing acircuit offset voltage V_(CIRCUIT), equal to the voltage drop acrossresistor R₃. The values of voltage V₄ and resistor R₄ are chosen to makeV_(CIRCUIT)>V_(OS). Therefore, when charge current is zero, V_(i) iszero, the charge controller 130 output V₀ is zero, V₁ is zero, V(+) isequal to V_(OS), (V−) is equal to V_(CIRCUIT), and (V−) is greater than(V+), so V₃ decreases to zero. At this point, the battery chargingcontrol circuit 110 may begin calibration to calculate a value for V₀that will produce a correct bias that can be applied to cancel out thevoltage offset V_(OS) of the op amp 120.

The charge controller 130 also includes an analog-to-digital converter(ADC) 134, which is used during calibration to sense the output V₃ of opamp 120. When battery charging is enabled, the calibration routine isrun first, before charging begins. During calibration, there is nocharge current, so V₃ is zero. The negative input (V−) of the op amp 120is set by V₄, R₄, and R₃ as (V−)=V₄×R₃/(R₃+R₄)=V_(CIRCUIT). Next, thecharge controller 130 enters a calibration cycle (shown in detail inFIG. 4), and uses the op amp 120 output voltage V₃ to set V₀, accordingto the following formula: V₀=K₁−(K₂×V₃), where K₁ and K₂ are constants.In an example, during calibration, V₀ and V₃ are each limited within adefined operational range.

Initially, V₃ is zero, so V₀ steps up to voltage K₁. This chargescapacitor C₁, and consequently V₁ increases toward a voltageV₁=V₀×R₂/(R₁+R₂). This V₁ is summed with Vos to make (V+)=V1+Vos. The opamp 120 then amplifies the difference between the positive and negativeterminals (V+) and (V−), resulting in output V₃. As (V+) begins toexceed (V−). V₃ rises, but the rate of rise is slowed by capacitor C₂.As V₃ in turn rises, the charge controller 130 samples V₃; when V3 riseswithin a certain range, the charge controller 130 sets V₀ lower, whichlowers V₁. The circuit time constants are set such that the op ampoutput V₃ settles into regulation to a steady state value, which cancelsthe total offset (circuit offset plus V_(OS)). The voltage versus timeplots of V₀, V₁, and V₃ are illustrated in FIG. 2.

In this condition, the steady state output from the charge controller130 (V₀), is the value needed to cancel V_(CIRCUIT)+V_(OS), the circuitand op amp offsets (which are equal to V₁). This value of V₀ is storedin a memory of the charge controller (not shown), and calibration of thebattery charging control circuit 110 is complete. In examples, V₃ may beprevented from rising high enough to turn on transistor Q₁, thuspreventing any incidental battery charging during the calibrationprocess.

During the calibration process, the op amp 120 is configured as an erroramplifier, just as when used as a current regulator, except that thefunctions of the inputs (V+) and (V−) are inverted as shown in FIG. 1.The op amp 120 senses the feedback voltage V₁ at (V+), and compares itto the reference voltage V₄×R₃/(R₃+R₄) at (V−). The voltage differencebetween terminals (V+) and (V−) is amplified and output as voltage V₃,which drives other elements to control the voltage V₁. The chargecontroller 130, resistor R₁, resistor R₂, and capacitor C₁ control theamount, and frequency response, of the amplification by the op amp 120.Because this feedback is input to the (V+) terminal of the op amp, theprocedure provides the phase reversal to cause the negative feedbackneeded to achieve regulation. If the feedback V₁ is greater than thereference (V−), then V₃ is increased so that the charge controller 130causes V₀ to be reduced. This in turn reduces V₁, thus regulating V₁ tovirtually equal (V−), which equals the circuit and op amp offsets. Thisprocess measures the total offset voltage and identifies the steadystate value of V₀ needed to cancel the effects of the battery chargingcontrol circuit's 110 offsets. In this manner, the op amp 120automatically identifies the offset voltage of the battery chargingcontrol circuit 110 and op amp 120.

After calibration of the battery charging control circuit 110, thebattery charging begins. The stored value V₀ is used as a fixed offsetterm (a voltage bias value) to set the charge current. The chargecontroller 130 output V₀ is set equal to a constant K₃ times the desiredcharge (I_(d)) current plus the stored voltage bias value (e.g.,(K₃×I_(d))+V_(bias)). In this way, a battery charging current issupplied to the battery 104 via the battery charger 102 responsive tothe battery charger receiving a control signal representative of thevoltage from the battery charging circuit.

FIG. 2 illustrates a plot of the calibrated circuit offset biasaccording to examples of the present disclosure. In the example shown,voltage V₀ starts out at an initial value of 1.32 volts and remainsconstant for the first 40-50 milliseconds as capacitor C₁ is charging.Meanwhile, during an approximately similar period of time, capacitor C₂is charging as shown by the plot of V₁. Once capacitor C₁ is charged,the voltage V₀ drops to a steady value of 17.9 millivolts. During thecharging time of the capacitors C₁ and C₂, the output of the op amp V₃gradually rises as V₀ decreases. Between the roughly 80-100 millisecondrange, V₃ begins to stabilize, which is reflected by V₀ stabilizing. Inthis example, the value of V₀ represents a voltage bias value of 0.69volts. It should be understood that the values and plots shown in theexample of FIG. 2 are merely intended as being one possible exampleimplementation of the techniques described herein and should not beconstrued as limiting.

FIG. 3 illustrates a flow diagram of a method for regulating batterycharging current according to examples of the present disclosure. Themethod 300 may be executed by a computing system such as computingsystem 100 of FIG. 1 or may be stored as instructions on anon-transitory computer-readable storage medium that, when executed by aprocessor, cause the processor to perform the method 300. In oneexample, method 300 may include: initiating a battery charging (block302); calibrating a battery charging circuit (304); determining adesired charge (306); using a voltage input to an op amp to controlcharge current (block 308); supply battery charging current (block 310);and determining whether the charge is complete (block 312).

At block 302, the method 300 includes initiating a battery charging.Battery charging may be initiated, for example, by a battery charger(e.g. battery charger 102 of FIG. 1) of a computing system (e.g.,computing system 100 of FIG. 1) being plugged into a power source (e.g.,V_(IN) of FIG. 1). The method 300 continues to block 304.

At block 304, the method 300 includes calibrating a battery chargingcircuit. The calibration process is described below with reference toFIG. 4. Generally, the calibration process may include reading an outputvoltage of an op amp (block 402 of FIG. 4); determining whether theoutput voltage is stable (block 404 of FIG. 4); adjusting the inputvalue of the op amp when the output voltage is not stable (block 406 ofFIG. 4); and storing the input voltage value as a voltage bias valuewhen the output voltage is stable (block 408 of FIG. 4).

The battery charging circuit, in examples, may include an operationalamplifier having a negative input to receive a pre-bias voltage, apositive input, an output, and a voltage offset. The battery chargingcircuit may further include a charge controller having ananalog-to-digital converter to receive a voltage output from the outputof the operational amplifier and a voltage supply to supply a voltageinput into the positive input of the operational amplifier, wherein thevoltage input is a function of the voltage input. The voltage supply maybe a digital-to-analog converter in some examples or a pulse widthmodulator in other examples. The method 300 continues to block 306.

At block 306, the method 300 includes determining a desired chargecurrent for the battery charging circuit. The method 300 continues toblock 308.

At block 308, the method 300 includes using op amp voltage input toapply the desired charge current to regulate the charge current to thebattery charger (e.g., battery 102 of FIG. 1). The method continues toblock 310.

At block 310, the method 300 includes supplying a battery chargingcurrent to the battery. For example, the battery charger 102 may supplya battery charge current to a battery (e.g., battery 102 of FIG. 1),with the charge current being dependent upon the battery chargingcircuit calibration and voltage bias value. The method continues toblock 312.

At block 312, the method 300 includes determining whether the charge iscomplete, and if the charge is not complete, the method 300 returns toblock 306 to determine the desired charge and continue charging thebattery (e.g., battery 104 of FIG. 1). If the charge is complete, thebattery charger (e.g., battery charger 102) discontinues charging thebattery (e.g., battery 104 of FIG. 1).

Additional processes also may be included, and it should be understoodthat the processes depicted in FIG. 3 represent illustrations, and thatother processes may be added or existing processes may be removed,modified, or rearranged without departing from the scope and spirit ofthe present disclosure.

FIG. 4 illustrates a flow diagram of the calibration process of themethod for regulating current in a circuit such as the battery chargingcircuit of FIG. 3 according to examples of the present disclosure. Themethod 400 may be executed by a computing system such as computingsystem 100 of FIG. 1 or may be stored as instructions on anon-transitory computer-readable storage medium that, when executed by aprocessor, cause the processor to perform the method 400. In oneexample, method 400 may include: reading an output voltage of an op amp(block 402); determining whether the output voltage is stable (block404); adjusting the input value of the op amp when the output voltage isnot stable (block 406); and storing the input voltage value as a voltagebias value when the output voltage is stable (block 408).

At block 402, the method 400 includes reading an output voltage of an opamp (e.g., op amp 120 of FIG. 1). For example, a computing system (e.g.,computing system 100 of FIG. 1) may read a voltage output (e.g., voltageV₃ of FIG. 1) using an analog-to-digital converter of the computingsystem (e.g. ADC 134 of charge controller 130 of FIG. 1). The method 400continues to block 404.

At block 404, the method 400 includes determining whether the outputvoltage is stable. For example, responsive to determining that thevoltage output from the operational amplifier in a current regulatingcircuit is not stable, the computing system (e.g., computing system 100of FIG. 1) inputs a voltage input (e.g., voltage V₀ of FIG. 1) into theoperational amplifier (e.g., op amp 120 of FIG. 1) in the currentregulating circuit equal to a first constant value minus the voltageoutput times a second constant value until the voltage output is stable(block 406). The voltage input may be generated by a digital-to-analogconverter in some examples or by a pulse width modulator in otherexamples (e.g., voltage source 132 of the charge controller 130 of FIG.1). The stable voltage output may not be limited or clamped by theoutput voltage range of the op amp in some examples. The method 400continues to block 408.

At block 408, the method 400 includes storing the input value of the opamp when the output voltage is stable. For example, responsive todetermining that the voltage output from the operational amplifier inthe current regulating circuit is stable, the computing system (e.g.,computing system 100 of FIG. 1) stores the voltage output (e.g., voltageV₃ of FIG. 1) as a voltage bias value, which may be utilized in acurrent regulating circuit (e.g. battery charging control circuit 110 ofFIG. 1) to cancel an offset voltage in the operational amplifier.

Additional processes also may be included. For instance, it may again bedetermined whether the voltage output from the operational amplifier inthe battery charging circuit is stable responsive to inputting thevoltage input into the operational amplifier. It should be understoodthat the processes depicted in FIG. 4 represent illustrations, and thatother processes may be added or existing processes may be removed,modified, or rearranged without departing from the scope and spirit ofthe present disclosure.

It should be emphasized that the above-described examples are merelypossible examples of implementations and set forth for a clearunderstanding of the present disclosure. Many variations andmodifications may be made to the above-described examples withoutdeparting substantially from the spirit and principles of the presentdisclosure. Further, the scope of the present disclosure is intended tocover any and all appropriate combinations and sub-combinations of allelements, features, and aspects discussed above. All such appropriatemodifications and variations are intended to be included within thescope of the present disclosure, and all possible claims to individualaspects or combinations of elements or steps are intended to besupported by the present disclosure.

What is claimed is:
 1. A method comprising: determining, by a computingsystem, whether a voltage output from an operational amplifier in acurrent regulating circuit is stable, wherein stability is determined bywhether the voltage output changes at a rate beyond a predeterminedoperational level desired for a rechargeable battery, the voltage beingread by an analog-to-digital converter of the computing system, whereinthe operational amplifier having a negative input to receive a pre-biasvoltage, a positive input, an output, and a voltage offset, and whereinthe pre-bias voltage received at the negative input of the operationalamplifier is greater than half the range of the voltage offset of theoperational amplifier; responsive to determining that the voltage outputfrom the operational amplifier in the current regulating circuit is notstable, inputting, by the computing system, a voltage input into theoperational amplifier in the current regulating circuit equal to a firstconstant value minus the voltage output times a second constant valueuntil the voltage output is stable; and responsive to determining thatthe voltage output from the operational amplifier in the currentregulating circuit is stable, storing, by the computing system, thevoltage output value as a voltage bias value to cancel an offset of thecurrent regulating circuit.
 2. The method of claim 1, wherein thecurrent regulating circuit is a battery charging circuit.
 3. The methodof claim 1, wherein the voltage input is generated by adigital-to-analog converter.
 4. The method of claim 1, wherein thevoltage input is generated by a pulse width modulator.
 5. The method ofclaim 1, further comprising: responsive to inputting the voltage inputinto the operational amplifier, determining, by the computing system,whether the voltage output from the operational amplifier is stable. 6.A computing system comprising: a battery charger electrically coupled toa battery and a battery charging circuit, the battery charging circuitfurther comprising: an operational amplifier having a negative input toreceive a pre-bias voltage, a positive input, an output, and a voltageoffset, wherein the pre-bias voltage received at the negative input ofthe operational amplifier is greater than the half the range of thevoltage offset of the operational amplifier; and a charge controllerhaving an analog-to-digital converter to receive a voltage output fromthe output of the operational amplifier and a voltage supply to supply avoltage input into the positive input of the operation amplifier tocancel the voltage offset of the operational amplifier, wherein thecharge controller determines whether the voltage output from theoperational amplifier in the battery charging circuit is stable, whereinstability is determined by whether the voltage output changes at a ratebeyond a predetermined operational level desired for a rechargeablebattery, and wherein the voltage output of the charge controller is afunction of the voltage input of the charge controller.
 7. The system ofclaim 6, wherein the voltage supply is a digital-to-analog converter. 8.The system of claim 6, wherein the voltage supply is a pulse widthmodulator.
 9. A method, comprising: initiating, by a computing system, abattery charging for a rechargeable battery; calibrating, by thecomputing system, a battery charging circuit, the battery chargingcircuit further comprising: an operational amplifier having a negativeinput to receive a pre-bias voltage, a positive input, an output, and avoltage offset, wherein the pre-bias voltage received at the negativeinput of the operational amplifier is greater than the half the range ofthe voltage offset of the operational amplifier, and a charge controllerhaving an analog-to-digital converter to receive a voltage output fromthe output of the operational amplifier and a voltage supply to supply avoltage input into the positive input of the operation amplifier,wherein the charge controller determines whether the voltage output fromthe operational amplifier in the battery charging circuit is stable,wherein stability is determined by whether the voltage output changes ata rate beyond a predetermined operational level desired for therechargeable battery; determining, by the computing system, a desiredcharge current for the battery charging circuit; applying, by thecomputing system, the desired charge current to the battery chargingcircuit to cancel the voltage offset of the battery charging circuit;and supplying, by the computing system, a battery charging current tothe battery.
 10. The method of claim 9, wherein the voltage output ofthe charge controller is a function of the voltage input of the chargecontroller.
 11. The method of claim 9, further comprising: determining,by the computing system, whether the battery charging is complete. 12.The method of claim 11, further comprising: responsive to determiningthat the battery charging is not complete, determine a desired currentcharge for the battery charging circuit; apply the voltage to controlthe battery charging current; and supply the battery charging current tothe battery.
 13. The method of claim 9, wherein the voltage supply is adigital-to-analog converter.
 14. The method of claim 9, wherein thevoltage supply is a pulse width modulator.
 15. The method of claim 9,comprising calibrating the battery charging circuit to determine a levelof battery charging current to supply to the rechargeable battery.